A Spectral Theory for Certain Operators on a Direct Sum of Hilbert Spaces

1966 ◽  
pp. 294-330
Author(s):  
Nelson Dunford
Keyword(s):  
Spectral Theory ◽  
Hilbert Spaces ◽  
Direct Sum

scholarly journals Lorentz-Marcinkiewicz property of direct sum of operators

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 391-398
Author(s):  
Ala Ipek
Keyword(s):  
Hilbert Spaces ◽  
Direct Sum

In this paper, the relations between Lorentz-Marcinkiewicz property of the direct sum of operators in the direct sum of Hilbert spaces and its coordinate operators are studied. Then, the obtained results are supported by applications.

Geršgorin theory and the definiteness of determinantal operators

1987 ◽  
Vol 106 (1-2) ◽  
pp. 1-10 ◽  
Author(s):  
D. R. Farenick ◽  
Patrick J. Browne
Keyword(s):  
Spectral Theory ◽  
Hilbert Spaces ◽  
Diagonal Dominance ◽  
Dominance Properties

SynopsisLet Aij, l≦j≦k, be bounded Hermitean operators on Hilbert spaces Hi, 1≦i≦k, and let be the induced operators on . An important operator for multiparameter theory is δ: H →H denned by δ = det the determinant being expanded formally. Various definiteness properties of δ are critical for multiparameter spectral theory.We use the operators Aij to construct a numerical matrix δ(δ) upon which we use Geršgorin theory to investigate the non-singularity and definiteness of δ. Diagonal dominance properties of the array [Aij] are also discussed.

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